Gauge invariant investigation of the nature of Confinement

We observe a strong correlation between the decrease in the number of action density peaks in SU(2) Yang-Mills configurations with cooling and that of the string tension. The nature and distribution of these peaks is investigated. The relationship with monopole currents after the abelian projection is also considered.Comment: uuencoded and Z-compressed file of the Postcript version of our contribution to LATTICE 95. 4 pages of text and 4 figure

Higgs bundles for the Lorentz group

Using the Morse-theoretic methods introduced by Hitchin, we prove that the moduli space of \SO_0(1,n)-Higgs bundles when $n$ is odd has two connected components

Volume dependence in 2+1 Yang-Mills theory

We present the results of an analysis of a 2+1 dimensional pure SU(N) Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial magnetic flux. We focus on investigating the dependence of the electric-flux spectrum, extracted from Polyakov loop correlators, with the spatial size l, the number of colours N, and the magnetic flux m. The size of the torus acts a parameter that allows to control the onset of non-perturbative effects. In the small volume regime, where perturbation theory holds, we derive the one-loop self-energy correction to the single-gluon spectrum, for arbitrary N and m. We discuss the transition from small to large volumes that has been investigated by means of Monte-Carlo simulations. We argue that the energy of electric flux e, for the lowest gluon momentum, depends solely on e/N and on the dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The variable x can be interpreted as the dimensionless 't Hooft coupling for an effective box size given by Nl. This implies a version of reduction that allows to trade l by N without modifying the electric-flux energy.Comment: 7 pages, 3 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia. Minor change: Fig. 1 modified to correctly account for the sign convention in Eq. (2.5

Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics

We present a detailed study of a filtering method based upon Dirac quasi-zero-modes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte Carlo dynamics on topological structures like instantons.Comment: 39 pages, 15 figure